In this work, we explore and propose several quantum circuit mapping strategies to optimize qubit shuttling in scalable quantum computing architectures based on silicon spin qubits. Our goal is to minimize phase errors introduced during shuttling operations while reducing the overall execution time of quantum circuits. We propose and evaluate five mapping algorithms using benchmarks from quantum algorithms. The Swap Return strategy emerged as the most robust solution, offering a superior balance between execution time and error minimization by considering future qubit interactions. Additionally, we assess the importance of initial qubit placement, demonstrating that an informed placement strategy can significantly enhance the performance of dynamic mapping approaches.

In this paper, we present a fully integrated ring-oscillator (RO)-based temperature sensor for quantum computing applications. As the quantum states exhibit an exponential sensitivity to the on-die cryogenic temperature change, any such temperature variation due to, for example, local heating islands arising from the poor thermal conductivity of silicon should be monitored. For this purpose, we exploit a compact RO sensor placed in the vicinity of qubits. The proposed approach employs four differently sized oscillators and two VBGs to generate, in total, eight different temperature-dependent oscillating frequency signals. Then, by performing their polynomial fitting, a linear temperature-frequency compensating model for the proposed sensor is derived. Fabricated in 22 nm FD-SOI technology, the proposed sensor occupies 0.0016 mm2, consumes 128 μW and achieves maximum inaccuracy of ± 2.1 K in a wide temperature range from 3 to 270 K.

In this paper, we present an inverter-based ring oscillator (RO) operating at cryogenic temperatures for quantum computing applications. It employs a low-dropout regulator (LDO) to provide supply voltage for a programmable switched-capacitor system which isolates the supply line of the integrated RO circuit from any noise or perturbations of the external power supply. In anticipation of embedding the RO into a phase-locked loop (PLL), we study the variation of flicker phase noise from cryo to room temperature by indirectly measuring the phase noise (PN) in the 30dB/dec region. The proposed system occupies 0.012mm2and shows 3.5dB integrated PN improvement thanks to the proposed voltage supply noise reduction technique at room temperature (RT) and the FOM is estimated as 121.7dB at cryogenic temperature (CT).

Quantum computers promise to revolutionize information processing, offering game-changing opportunities in fields such as cryptography, machine learning, drug discovery, etc. However, building large-scale quantum computers presents significant challenges, requiring both fundamental research and technological breakthroughs. Among the various platforms proposed for the realization of the core of the quantum hardware, qubits realized in semiconductor nanostructures stand out. One of their key advantages lies in their compatibility with standard semiconductor manufacturing, enabling, among other capabilities, their co-integration with control and readout electronics, thus improving scalability and reducing interconnect complexity. In this review, we discuss recent advances in silicon-based spin qubits and present an overview of the progress and challenges in developing large-scale quantum computing systems based on this architecture.

In this paper, we present the characterisation of ring oscillator (RO) test circuits fabricated in GlobalFoundries’ (GF) 22nm fully depleted silicon-on-insulator (FD-SOI) process and operating from 200 K down to 4 K. We investigate ROs using NAND, NOR, and inverter standard cell libraries, including low, regular, and high threshold-voltage versions. Alongside temperature variations, we also consider a change in the power supply of ±5% from a nominal 0.8 V. The ROs demonstrate the combined effect of increased mobility, increased threshold voltage, and leakage current processes at cryogenic temperatures on their operation. By averaging over 81 fabricated ROs using three different delay gates and 2 different flavours, we report a statistical characterisation of their properties in the FD-SOI technology over temperature and supply voltage.

The grand challenge of scaling up quantum computers requires a full-stack architectural standpoint. In this position paper, we will present the vision of a new generation of scalable quantum computing architectures featuring distributed quantum cores (Qcores) interconnected via quantum-coherent qubit state transfer links and orchestrated via an integrated wireless interconnect.

This paper proposes the use of a tunable$LC$resonator to read an array of qubits in a multiplexed fashion, by making the dispersive shift of the targeted qubit dominant. Cavity and circuit electrodynamics (QED) theory is shown to support this idea. The tunable capacitor array, in parallel with a superconducting inductance, is designed to maximize the quality factor by frequency range product,$Q\cdot\Delta\omega$. This approach only requires one RF signal to measure multiple qubits, which can facilitate quantum computing scaling.

This Special Issue is a collection of selected papers presented at the IEEE Asia Pacific Conference of Circuits and Systems (APCCAS) 2019 that was held in Bangkok, Thailand, November 11–14, 2019, and the IEEE International Conference on Electronics, Circuits and Systems (ICECS) 2019 that was held in Genova, Italy, on November 27–29, 2019. As the flagship conferences of the IEEE Circuits and Systems Society (CASS) in IEEE Regions 10 and 8, respectively, these conferences welcome contributions across the themes within the scope of the Society, including analog, digital, and mixed-signal electronics, signal processing, power electronics, communication theory, sensors, circuit theory, and nonlinear circuits and systems.

This Special Issue is a collection of selected papers presented at the IEEE Latin American Symposium on Circuits and Systems (LASCAS) 2020 that was held in San José, Costa Rica, on February 25–28, 2020. As the flagship conference of the IEEE Circuits and Systems Society (CASS) in IEEE Region 9, this conference welcomes contributions across the themes within the scope of the society, including analog, digital, and mixed-signal electronics, signal processing, power electronics, communication theory, sensors, circuit theory, and nonlinear circuits and systems.

In this paper, we study networks of coupled oscillators applied to the distributed synthesis of clock signals for large systems-on-chip. The oscillators are implemented as interconnected all-digital phase-locked loops (ADPLLs), which are asynchronous control systems. We address the issue of modelling, synchronization and stability of both a single ADPLL and interconnected ADPLLs. We prove that the stability domain is universal for large Cartesian networks, and it related to the domain for a single ADPLL. We show that within the stability domain the network synchronises to the reference signal both in frequency and phase. A hardware verification of Cartesian networks is presented, and it is consistent with our theoretical findings. The proposed design may be useful for multiples engineering and physics applications, including clock generation, distributed computations, beamforming, and other applications, where the control over time synchronicity is crucially important for the system performance.

In this paper we demonstrate electrostatic control and feasibility of entanglement in CMOS qubits. We present both single particle and multi-particle methodologies to describe quantum transport using a time-dependent Hamiltonian assuming one spatial degree of freedom. The developed models predict maximally entangled states of electrons controlled electrostatically by external driving fields and interacting via the Coulomb force.

We describe a quantum computing hardware paradigm that exploits the current scaling achievements of mainstream CMOS technology. Just like in a small IC chip, where a single nanometer-sized CMOS transistor can be reliably replicated millions of times to build a digital processor, we propose a new structure of a qubit realized as a CMOS-compatible charge-based quantum dot that can be reliably replicated thousands (or perhaps even millions) of times to construct a quantum processor. Combined with an on-chip CMOS controller, it will realize a useful quantum computer (QC) that can operate at 4 K, which is much higher than the temperature of today's QCs of 15 mK.

This work is aimed at the development of a path-based approach to Statistical Static Timing Analysis. Timing Analysis is an absolutely essential step in the verification of Very Large Scale Integration (VLSI) designs. We propose a novel analytical methodology for the fast calculations of VLSI delay. The problem is stated in such a way that becomes equivalent to finding the maximum of a large set of correlated random variables (RVs). For this purpose, a corresponding extension of extreme value theory of weakly-correlated RVs is developed. Results of simulations showing a comparison of our approach with Monte Carlo simulations are presented. Possible applications, extensions of our methodology and future steps are discussed.

Magnetic components are essential in many applications of electronics. Despite a very clear understanding of magnetic phenomena developed from first principles of Electromagnetics and Maxwell's equations, modelling of the magnetic field, flux and force in a particular system can be a very challenging problem. Often, direct calculations are avoided, and a phenomenological model describing magnetic interactions is used instead. There are a number of methods which can be used for the modelling of the magnetic field due to magnetic materials and inductors and which can provide detailed and predictive information on such systems. Multi-physics scientific packages utilising finite-element methods are among the most common tools as they can solve a wide range of different problems and employ universal numerical algorithms. As a trade-off, they are very resource-intensive and have a low speed of execution. As an alternative, one can develop simulation techniques utilising magnetic dipoles or equivalent currents. These methods are less resource-intensive and very fast; however, they also have their limitations. This paper presents a method of equivalent currents developed for the fast calculation of the magnetic field and flux. We show the application of the method to inductors and permanent magnets that have a particular importance in power electronics and electromagnetic kinetic energy harvesting.

Microelectromechanical systems contain mechanical elements coupled with conditioning electronics that control and process the signal generated by the mechanical component. These systems are miniature and can be easily integrated on one chip, which explains the enormous popularity of MEMS. The applications of MEMS began with environmental sensors and have grown to encompass RF and optical applications along with energy harvesting. Because of their mixed-domain nature, the design of conditioning electronics relies on accurate models of the mechanical component. As an additional requirement, the model must be simple enough and be compatible with common circuit simulation tools. The latter requirement may be particularly difficult to achieve due to the fact that most of modern MEMS structures are quite complex and often nonlinear. In this conference contribution, we describe the methodology of building a model of a nonlinear MEMS resonator using the conventional modelling approach and then using an improved model together with an optimisation technique on the basis of the circuit simulator PAN.

In this paper, we introduce a statistical approach for studying a special class of nonlinear dynamical systems such as ADPLLs and ADPLL networks, where the process driving the adjustment of the DCO frequency can be seen as ΣΔ modulation. We showed that, by applying the Frobenius-Perron operator to the governing equation, it is possible to find the invariant probability density which is valid for dynamically changing input of Σmodulator. By using this, we show that the average behaviour of the corresponding complex system can be dramatically simplified and studied analytically.

In this paper, we propose the model of a network consisting of All-Digital Phase-Locked Loop Network in application to Clock-Generating Systems. The method is based on a solution of a system of non-linear finite-difference stochastic equations and allows us to perform high speed simulations of a distributed Clock Network on arbitrary topology. The result of our analysis show a good agreement with experimental measurements of a 65nm CMOS All-Digital Phase-Locked Loop Network.

In this paper we consider a network of phase oscillators. We develop the equations that model the time evolution of the phase of each oscillator in the network. The oscillator represents a modified Kuramoto oscillator and in this study we discuss how these modifications are obtained. In the context of this study, we use this network to model a network of PLLs for distributed clock applications. We analyse analytically and numerically the synchronisation modes of this system for different types of the coupling function. We show that depending on the properties of the coupling function, the network displays either multiple coexisting synchronisation modes or only a single synchronisation mode. While in the context of clock generation, multiple synchronisation modes coexisting in the system at the same parameters are a parasitic phenomenon. However in the context of other application such as associative memory models, mode-locking can be seen a useful phenomenon. The results provide a deeper understanding of globally synchronised clock networks with applications in microprocessor design.

The aim of this paper is to formalise the term “complexity” in the context of modern microelectronics, propose the definitions of key terms and discuss a case study. Our aim is to show that the term “complex system” is implicitly related to the design of electronic systems.

In this work we investigate the dynamics of a floating electrode microelectromechanical (MEMS) switch. This is a type of very common MEMS that are actuated electrostatically, i.e., by applying a voltage across the micromechanical structure. A floating electrode MEMS is a novel modification of a capacitive switch where a thin metal layer is deposited on top of the isolating dielectric layer. Although these devices have promising characteristics, this modification alters their behaviour in comparison with conventional MEMS switches. We develop a multi-physics model to simulate the behaviour of the switch and model a number of physical effects that occur in the system and influence its dynamics. We used a fractal as representation of the electrode surface to model the field emission as a result of a local enhancement of the electric field. We provide the comparison of the simulated behaviour with experimental results.

Transitions to chaos in one-dimensional maps are known to occur in a universal fashion. This transition can be described symbolically by a sequence of words known as the U-sequence. In this work we investigate the appearance of this U-sequence in a class of electronic oscillators that describe the dynamics of electrostatic vibration energy harvesters. We show how the method of symbolic dynamics is applied to systems described by ODEs and further, we investigate why the U-sequence is not fully followed by this class of oscillators that contain a non-conservative damping force.

In this paper, we overview the sources of nonlinearities and the methods of analysis for electrostatic (capacitive) vibration energy harvesters by the example of an energy harvester employing a charge pump base conditioning circuit. Electrostatic vibration energy harvesters are devices that contain mechanical resonators driven by ambient vibrations and coupled with conditioning electronic circuits through a capacitive transducer. These devices are characterised by internal and external nonlinearity and complexity and can display irregular behaviour. We give an overview of the capacitive conversion mechanisms and discuss the nonlinear techniques that can be employed for the analysis of nonlinear vibration energy harvesters.

This paper presents an overview of problems related to electronic conditioning of capacitive transducers used for the kinetic energy conversion. It proposes a methodology for the system-level and circuit-level design of conditioning electronics for electrostatic energy harvesters so to comply with the requirements of realistic applications: long-lasting operation, self-calibration, low consumed power and the implementation using the integrated circuit CMOS technology. An original architecture of a self-calibrating conditioning circuit is proposed. The paper gives a review of main design challenges related to this architecture, explains the motivation of the technology choice, provides insight into critical blocks and presents intermediate results of design.

In this review paper, we define and discuss the concept of complexity for heterogeneous systems. Due to the current progress in fabrication technology, modern micro-scale integrated systems may have a large number of interacting elements. Each of those elements not only displays its own dynamical properties, but also, in the most general case, can be nonlinear or can belong to different physical domains. We consider two different examples of systems that are complex in the terms we use in this paper. The first example is a network of oscillators and is heterogeneous since it is a mixed-signal system. The second example is an electrostatic vibration energy harvester, a micro scale system combining elements from the mechanical and electrical domains. In both cases we discuss the challenges that arise at the stage of the system design.

Dielectric charging of insulating films in micro-electromechanical systems (MEMS) has a crucial effect on the operation of those devices. In our previous work we have shown the feasibility of a new sigma-delta based control method which is able to maintain the dielectric charge at a desired level. The method is based on a smart actuation technique where the applied voltage is selected based on the state of the device. The purpose of this paper is to show the link between the method and sigma-delta modulation and to investigate the operation of the method in the space of device parameters.

Vibration energy harvesting is a technique for the generation of electricity from ambient vibrations. Electrostatic vibration energy harvesters (e-VEHs) are particularly compatible with microtechnology and can serve as a source of energy for autonomous microsystems. E-VEHs require conditioning electronics to effectively sequence different phases of energy conversion. One of the most promising circuits for e-VEHs is the charge pump, presented here with a resistive return circuit. E-VEH as a system is composed of a mechanical resonator coupled with a conditioning circuit and is strongly nonlinear. We discuss different models of this system and show how steady-state oscillations of the system can be analysed. In order to do so, the system is represented as a nonlinear oscillator and a perturbation technique, such as the multiple scales method, can be applied.

The aim of this paper is to study an electrostatic vibration energy harvester that utilises a nonlinear resonator. A vibration energy harvester represents a system where a mechanical resonator driven by ambient vibrations is coupled with a conditioning electronic circuit, which acts as a damper and converts mechanical energy into electrical. If a nonlinear resonator is embedded into the conditioning circuit, nonlinearity will appear from both mechanical and circuit components of the system. We expand the analytical approach that we developed in our previous works to the case of combined mechanical and circuit nonlinearities. This allow us to analyze steady-state behavior and compare it with the linear case. In addition, we discuss a specific nonlinear phenomena that is introduced by the discontinuity of the system - the sliding bifurcation. We show that the onset of steady-state quasi-harmonic oscillations occur through the disappearance of sliding motion.

In this review paper, we discuss the principles of electrostatic (capacitive) vibration energy harvesters and nonlinear techniques that can be applied to improve the performance of harvesters. Electrostatic vibration energy harvesters are devices that contain mechanical resonators driven by ambient vibrations and coupled with conditioning electronic circuits through a capacitive transducer. While the devices can be fabricated using MEMS technology and miniaturised, internal and external nonlinearity and complexity can lead to irregular behavior and impede the analysis of the devices. In this review we give an overview of the capacitive conversion mechanisms, discuss the basic triangular energy conversion cycle in detail and survey the nonlinear techniques that can be employed in these systems.

In this paper, we present an analysis of an electrostatic vibration harvester operating in the constant-charge mode. The goal of the study is to bound regions of control parameters where the system displays steady-state harmonic oscillations as required for practical use. We show how the system can be presented as a nonlinear oscillator and analysed employing the multiple scales method, Floquet theory and Lyapunov exponents. We determine the conditions for the onset of steady-state oscillations, the period doubling bifurcation and transition to chaos. This allows us to bound regions of control parameters where the system displays desired regular oscillations and, therefore, to identify maximal harvestable power for a particular architecture.

In this work, we consider a system that consists of a microresonator and a Σ Δ type feedback loop control which is typically a part of inertial sensors. We describe this architecture as a dynamical system (an iterative difference equation) in the time domain in order to study possible periodic solutions in the output.

In this paper, we study the possible output of the pulsed digital oscillator (PDO) with multiple resonant modes of the mechanical resonator in the feedback loop. PDOs are simple circuits that allow linear resonators to maintain self-sustained oscillations and can work as mass-change resonant sensors. For a resonant sensor, activation of higher vibration modes of a mechanical resonator can be a way to improve its performance. We show that the location of the sensing/actuation system affects the output and can enhance higher mechanical modes.

In this paper we apply methods of nonlinear dynamics to examine the behavior of the pulsed digital oscillator for microelectromechanical systems (MEMS). We study the regions of existence of oscillations and demonstrate the effect on these of including additional delays into the feedback loop.